35th@MSC2020-3：分析学@20260125
| 26-XX Real functions [See also 54C30] 26-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to real functions 26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions 26-02 Research exposition (monographs, survey articles) pertaining to real functions 26-03 History of real functions [Consider also classification numbers pertaining to Section 01] 26-04 Software, source code, etc. for problems pertaining to real functions 26-06 Proceedings, conferences, collections, etc. pertaining to real functions 26-08 Computational methods for problems pertaining to real functions 26-11 Research data for problems pertaining to real functions |
26-XX 实函数 [另见 54C30] 26-00 与实际功能相关的通用参考文献（手册、词典、参考书目等）
26-01 实函数相关导论性阐述（教材、辅导论文等）
26-02 关于实函数的研究文献（专著、综述文章）
26-03 实函数的历史 [另请参阅第01节中的分类编号]
26-04 与实际功能相关问题的软件、源代码等
26-06 与实函数相关的会议记录、会议论文集等
26-08 实函数相关问题的计算方法
26-11 实函数相关问题的研究数据
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| 26Axx Functions of one variable 26A03 Foundations: limits and generalizations, elementary topology of the line 26A06 One-variable calculus 26A09 Elementary functions 26A12 Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48] 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 26A16 Lipschitz (H¨older) classes 26A18 Iteration of real functions in one variable [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 26A21 Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems [See also 28A15] 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives 26A30 Singular functions, Cantor functions, functions with other special properties 26A33 Fractional derivatives and integrals 26A36 Antidifferentiation 26A39 Denjoy and Perron integrals, other special integrals 26A42 Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 26A45 Functions of bounded variation, generalizations 26A46 Absolutely continuous real functions in one variable 26A48 Monotonic functions, generalizations 26A51 Convexity of real functions in one variable, generalizations 26A99 None of the above, but in this section |
26Axx 单变量函数 26A03 基础：极限与泛化，直线的初等拓扑学
26A06 一元微积分
26A09 基本函数
26A12 函数的增长率、无穷阶函数、缓慢变化函数 [另见 26A48]
26A15 一元实函数的连续性及相关问题（包括连续模、半连续性、间断性等）{关于由傅里叶系数决定的性质，参见42A16；关于由逼近性质决定的性质，参见41A25、41A27}
26A16 莱普希茨（H¨older）类
26A18 一元实函数的迭代 [另见 37Bxx、37Cxx、37Exx、39B12、47H10、54H25]
26A21 实函数的分类；集合与函数的Baire分类[另见03E15、28A05、54C50、54H05]
26A24 分化（一元实函数）：一般理论、广义导数、中值定理[另见28A15]
26A27 无微分性（不可微函数，不可微点），不连续导数
26A30奇异函数、Cantor函数及其他特殊性质函数
26A33 分数导数与积分
26A36 抗分化
26A39 丹乔伊-佩龙积分及其他特殊积分 26A42 莱曼、斯蒂尔杰斯和勒贝格型积分 [另见 28-XX]
26A45 有界变分函数的泛化
26A46 一元绝对连续实函数
26A48 单调函数，推广
26A51 一元实函数的凸性，推广
26A99 上述均非，但本节适用
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| 26Bxx Functions of several variables 26B05 Continuity and differentiation questions 26B10 Implicit function theorems, Jacobians, transformations with several variables 26B12 Calculus of vector functions 26B15 Integration of real functions of several variables: length, area, volume [See also 28A75, 51M25] 26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) 26B25 Convexity of real functions of several variables, generalizations 26B30 Absolutely continuous real functions of several variables, functions of bounded variation 26B35 Special properties of functions of several variables, H¨older conditions, etc. 26B40 Representation and superposition of functions 26B99 None of the above, but in this section |
26Bxx 几个变量的功能 26B05 连续性与分化问题
26B10 内隐函数定理、雅可比行列式、多变量变换
26B12 向量函数的微积分
26B15 多变量实函数的积分：长度、面积、体积 [另见 28A75、51M25]
26B20 多元实函数积分公式（斯托克斯、高斯、格林等）
26B25 多变量实函数的凸性，推广
26B30 多变量绝对连续实函数，有界变差函数
26B35 多变量函数的特殊性质、H¨older条件等
26B40 函数的表示与叠加
26B99 上述均非，但本节
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| 26Cxx Polynomials, rational functions in real analysis 26C05 Real polynomials: analytic properties, etc. [See also 12Dxx, 12Exx] 26C10 Real polynomials: location of zeros [See also 12D10, 30C15, 65H05] 26C15 Real rational functions [See also 14Pxx] 26C99 None of the above, but in this section 26Dxx Inequalities in real analysis {For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15} 26D05 Inequalities for trigonometric functions and polynomials 26D07 Inequalities involving other types of functions 26D10 Inequalities involving derivatives and differential and integral operators 26D15 Inequalities for sums, series and integrals 26D20 Other analytical inequalities 26D99 None of the above, but in this section |
26Cxx 多项式，实分析中的有理函数 26C05 实多项式：解析性质等[另见12Dxx、12Exx]
26C10 实多项式：零点位置 [另见 12D10、30C15、65H05]
26C15 实有理函数 [另见14Pxx]
26C99 上述均非，但本节
26Dxx 实分析中的不等式 {关于极大值函数不等式，参见42B25；关于泛函不等式，参见39B72；关于概率不等式，参见60E15}
26D05 三角函数与多项式的不等式
26D07 涉及其他类型函数的不等式
26D10 涉及导数及微分与积分算子的不等式
26D15 等式、级数和积分的不等式
26D20 其他分析不等式
26D99 以上均非，但本节适用
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| 26Exx Miscellaneous topics in real functions [See also 58Cxx] 26E05 Real-analytic functions [See also 32B05, 32C05] 26E10 C∞-functions, quasi-analytic functions [See also 58C25] 26E15 Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx] 26E20 Calculus of functions taking values in infinitedimensional spaces [See also 46E40, 46G10, 58Cxx] 26E25 Set-valued functions [See also 28B20, 49J53, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx} 26E30 Non-Archimedean analysis [See also 12J25] 26E35 Nonstandard analysis [See also 03H05, 28E05, 54J05] 26E40 Constructive real analysis [See also 03F60] 26E50 Fuzzy real analysis [See also 03E72, 28E10] 26E60 Means [See also 47A64] 26E70 Real analysis on time scales or measure chains {For dynamic equations on time scales or measure chains, see 34N05} 26E99 None of the above, but in this section |
26Exx 实函数中的杂项问题[另见58Cxx] 26E05 实解析函数 [另见 32B05、32C05] 26E10 C∞函数、拟解析函数 [另见 58C25]
26E15 无限维空间上的函数计算[另见46G05,58Cxx]
26E20 无限维函数的微积分
空间 [另见46E40、46G10、58Cxx]26E25 集值函数 [另见28B20、49J53、54C60] {关于非光滑分析，参见49J52、58Cxx、90Cxx}
26E30 非阿基米德分析 [另见 12J25]
26E35 非标准分析 [另见 03H05、28E05、54J05]
26E40 构造实分析 [另见 03F60]
26E50 模糊实分析 [另见 03E72,28E10]
26E60 意味着 [另见 47A64]
26E70 时间尺度或测度链上的实分析{关于时间尺度或测度链上的动力学方程，参见34N05}
26E99 上述均非，但本节
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| 28-XX Measure and integration {For analysis on manifolds, see 58- XX} 28-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration 28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration 28-02 Research exposition (monographs, survey articles) pertaining to measure and integration 28-03 History of measure and integration [Consider also classification numbers pertaining to Section 01] 28-04 Software, source code, etc. for problems pertaining to measure and integration 28-06 Proceedings, conferences, collections, etc. pertaining to measure and integration 28-08 Computational methods for problems pertaining to measure and integration 28-11 Research data for problems pertaining to measure and integration |
28-XX 测量与集成{关于流形的分析，参见58-XX} 28-00 与测量和集成相关的通用参考文献（手册、词典、参考书目等）
28-01导论性阐述（教材、教程论文，等) 与测量和积分有关
28-02 研究性论文（专著、综述）：测量与整合相关
28-03 测量与积分的历史 [另请参阅第01节相关分类编号]
28-04 针对相关问题的软件、源代码等测积
28-06 会议记录、会议资料、文集等测积
28-08 与测度和积分相关问题的计算方法
28-11 测量与积分相关问题的研究数据
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| 28Axx Classical measure theory 28A05 Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28A10 Real- or complex-valued set functions 28A12 Contents, measures, outer measures, capacities 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24] 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 28A25 Integration with respect to measures and other set functions 28A33 Spaces of measures, convergence of measures [See also 46E27, 60Bxx] 28A35 Measures and integrals in product spaces 28A50 Integration and disintegration of measures 28A51 Lifting theory [See also 46G15] 28A60 Measures on Boolean rings, measure algebras [See also 54H10] 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 28A78 Hausdorff and packing measures 28A80 Fractals [See also 37Fxx] 28A99 None of the above, but in this section |
28Axx 古典测度论 28A05 集合类（Borel域、 σ 环等）、可测集、Suslin集、解析集 [另见03E15、26A21、54H05] 28A10 实值或复值集合函数 28A12 内容、测度、外测度、容量 28A15 抽象微分理论与集合函数的微分 [另见26A24] 28A20 可测与不可测函数、可测函数序列、收敛方式 28A25 测度及其他集合函数的积分 28A33 测度空间、测度的收敛性 [另见46E27、60Bxx] 28A35 乘积空间中的测度与积分 28A50 测度的积分与分解 28A51 提升理论 [另见46G15] 28A60 布尔环上的测度、测度代数 [另见54H10] 28A75 长度、面积、体积及其他几何测度理论 [另见26B15、49Q15] 28A78 Hausdorff测度与堆积测度 28A80 分形 [另见37Fxx] 28A99 本节不涉及上述内容 |
| 28Bxx Set functions, measures and integrals with values in abstract spaces 28B05 Vector-valued set functions, measures and integrals [See also 46G10] 28B10 Group- or semigroup-valued set functions, measures and integrals 28B15 Set functions, measures and integrals with values in ordered spaces 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14] 28B99 None of the above, but in this section |
28Bxx 抽象空间值的集合函数、测度与积分 28B05 向量值集合函数、测度与积分 [另见 46G10] 28B10 群或半群值集合函数、测度与积分 28B15 有序空间值的集合函数、测度与积分 28B20 集值集合函数与测度；集值函数积分；可测选择 [另见 26E25、54C60、54C65、91B14] 28B99 本节不涉及上述内容 |
| 28Cxx Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20] 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures 28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures [See also 22Axx, 43A05] 28C15 Set functions and measures on topological spaces (regularity of measures, etc.) 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 28C99 None of the above, but in this section |
28Cxx 具有附加结构空间上的集合函数与测度[另见46G12、58C35、58D20] 28C05 通过线性泛函（如Radon测度、Daniell积分等）的积分理论，表示集合函数与测度 28C10 拓扑群或半群上的集合函数与测度、Haar测度、不变测度[另见22Axx、43A05] 28C15 拓扑空间上的集合函数与测度（测度的正则性等） 28C20 无限维空间中的集合函数与测度及积分（如Wiener测度、高斯测度等）[另见46G12、58C35、58D20、60B11] 28C99 本节不涉及上述内容 |
| 28Dxx Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 60Fxx, 60G10] 28D05 Measure-preserving transformations {For measure-preserving transformations and dynamical systems, see 37A05} 28D10 One-parameter continuous families of measurepreserving transformations {For dynamical systems aspect, see 37A10} 28D15 General groups of measure-preserving transformations {For dynamical systems aspects, see 37A15} 28D20 Entropy and other invariants 28D99 None of the above, but in this section |
28Dxx 测度论遍历理论 [另见 11K50、11K55、22D40、37Axx、47A35、60Fxx、60G10] 28D05 测度保持变换 {关于测度保持变换与动力系统，参见37A05}
28D10 一参数连续测度保持变换族{关于动力系统方面，参见37A10}
28D15 保持测度的变换的一般群 {关于动力系统方面的内容，参见37A15} 28D20 熵及其他不变量
28D99 本节不涉及上述内容
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| 28Exx Miscellaneous topics in measure theory 28E05 Nonstandard measure theory [See also 03H05, 26E35] 28E10 Fuzzy measure theory [See also 03E72, 26E50, 94D05] 28E15 Other connections with logic and set theory 28E99 None of the above, but in this section |
28Exx 测度论中的杂项问题 28E05 非标准测度论 [另见 03H05,26E35]
28E10 模糊测度理论 [另见 03E72、26E50、94D05]
28E15 其他与逻辑和集合论的联系
28E99 本节不涉及上述内容
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| 30-XX Functions of a complex variable 30-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable 30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable 30-02 Research exposition (monographs, survey articles) pertaining to functions of a complex variable 30-03 History of functions of a complex variable [Consider also classification numbers pertaining to Section 01] 30-04 Software, source code, etc. for problems pertaining to functions of a complex variable 30-06 Proceedings, conferences, collections, etc. pertaining to functions of a complex variable 30-08 Computational methods for problems pertaining to functions of a complex variable [See also 65Exx] 30-11 Research data for problems pertaining to functions of a complex variable |
30-XX 复变函数 30-00 与复变量函数相关的通用参考文献（手册、词典、参考书目等）
30-01 复变函数相关导论性阐述（教材、辅导论文等）
30-02 关于复变量函数的研究文献（专著、综述文章）
30-03 复变函数研究进展史 [另请参阅第01节分类编号]
30-04 复变函数相关问题的软件、源代码等资料 30-06 复变函数相关会议论文集、学术汇编等文献 30-08 复变函数问题的计算方法研究 [另见65Exx] 30-11 复变函数相关问题的研究数据 |
| 30Axx General properties of functions of one complex variable 30A05 Monogenic and polygenic functions of one complex variable 30A10 Inequalities in the complex plane 30A99 None of the above, but in this section |
30Axx 复变函数的一般性质 30A05 复变函数的单基因与多基因函数 30A10 复平面上的不等式 30A99 本节不涉及上述内容 |
| 30Bxx Series expansions of functions of one complex variable 30B10 Power series (including lacunary series) in one complex variable 30B20 Random power series in one complex variable 30B30 Boundary behavior of power series in one complex variable; over-convergence 30B40 Analytic continuation of functions of one complex variable 30B50 Dirichlet series, exponential series and other series in one complex variable [See also 11M41, 42- XX] 30B60 Completeness problems, closure of a system of functions of one complex variable 30B70 Continued fractions; complex-analytic aspects [See also 11A55, 40A15] 30B99 None of the above, but in this section |
30Bxx系列复变函数扩展 30B10单复变量幂级数（含空缺级数）30B20单复变量随机幂级数 30B30单复变量幂级数的边界行为与超收敛性 30B40单复变量函数的解析延拓 30B50单复变量的狄利克雷级数、指数级数及其他级数[另见11M41、42-XX] 30B60函数完备性问题与单复变量函数系的闭包 30B70连分数的复解析特性[另见11A55、40A15] 30B99本节不涉及上述内容 |
| 30Cxx Geometric function theory 30C10 Polynomials and rational functions of one complex variable 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} 30C20 Conformal mappings of special domains 30C25 Covering theorems in conformal mapping theory 30C30 Schwarz-Christoffel-type mappings [See also 65E10] 30C35 General theory of conformal mappings 30C40 Kernel functions in one complex variable and applications 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C50 Coefficient problems for univalent and multivalent functions of one complex variable 30C55 General theory of univalent and multivalent functions of one complex variable 30C62 Quasiconformal mappings in the complex plane 30C65 Quasiconformal mappings in R n, other generalizations 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods 30C75 Extremal problems for conformal and quasiconformal mappings, other methods 30C80 Maximum principle, Schwarz’s lemma, Lindel¨of principle, analogues and generalizations; subordination 30C85 Capacity and harmonic measure in the complex plane [See also 31A15] 30C99 None of the above, but in this section |
30Cxx 几何函数理论 |
| 30Dxx Entire and meromorphic functions of one complex variable, and related topics 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable [See also 34Mxx, 37Fxx, 39-XX] 30D10 Representations of entire functions of one complex variable by series and integrals 30D15 Special classes of entire functions of one complex variable and growth estimates 30D20 Entire functions of one complex variable, general theory 30D30 Meromorphic functions of one complex variable, general theory 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D40 Cluster sets, prime ends, boundary behavior 30D45 Normal functions of one complex variable, normal families 30D60 Quasi-analytic and other classes of functions of one complex variable 30D99 None of the above, but in this section |
30Dxx 复变函数与亚纯函数及其相关主题 30D05 复平面上的函数方程、单复变解析函数的迭代与复合[另见34Mxx、37Fxx、39-XX] 30D10 用级数与积分表示单复变全函数 30D15 单复变全函数的特殊类与增长估计 30D20 单复变全函数的通论 30D30 单复变亚纯函数的通论 30D35 单复变亚纯函数的值分布与Nevanlinna理论 30D40 集群集、原端与边界行为 30D45 单复变正规函数与正规族 30D60 单复变拟解析函数及其他函数类 30D99 本节不涉及上述内容 |
| 30Exx Miscellaneous topics of analysis in the complex plane 30E05 Moment problems and interpolation problems in the complex plane 30E10 Approximation in the complex plane 30E15 Asymptotic representations in the complex plane 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane [See also 45Exx] 30E25 Boundary value problems in the complex plane [See also 45Exx] 30E99 None of the above, but in this section |
30Exx 复平面上的其他分析主题 30E05 复平面上的矩问题与插值问题 30E10 复平面上的逼近方法 30E15 复平面上的渐近表示 30E20 积分、柯西型积分、复平面上解析函数的积分表示 [另见 45Exx] 30E25 复平面上的边值问题 [另见 45Exx] 30E99 本节不涉及上述内容 |
| 30Fxx Riemann surfaces 30F10 Compact Riemann surfaces and uniformization [See also 14H15, 32G15] 30F15 Harmonic functions on Riemann surfaces 30F20 Classification theory of Riemann surfaces 30F25 Ideal boundary theory for Riemann surfaces 30F30 Differentials on Riemann surfaces 30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) [See also 20H10] 30F45 Conformal metrics (hyperbolic, Poincar´e, distance functions) 30F50 Klein surfaces 30F60 Teichmu¨ller theory for Riemann surfaces [See also 32G15] 30F99 None of the above, but in this section |
30Fxx 莱曼曲面 30F10 紧致莱曼曲面与一致化 [另见 14H15,32G15] 30F15 莱曼曲面上的调和函数 30F20 莱曼曲面分类理论 30F25 莱曼曲面的理想边界理论 30F30 莱曼曲面上的微分 30F35 富克斯群与自守函数（紧致莱曼曲面与一致化的相关方面）[另见 11Fxx，20H10,22E40,32Gxx，32Nxx] 30F40 克莱因群（紧致莱曼曲面与一致化的相关方面）[另见 20H10] 30F45 保角度量（双曲度量、庞加莱度量、距离函数）30F50 克莱因曲面 30F60 莱曼曲面的泰希米勒理论 [另见 32G15] 30F99 本节不涉及上述内容 |
| 30Gxx Generalized function theory 30G06 Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05] 30G12 Finely holomorphic functions and topological function theory 30G20 Generalizations of Bers and Vekua type (pseudoanalytic, p-analytic, etc.) 30G25 Discrete analytic functions 30G30 Other generalizations of analytic functions (including abstract-valued functions) 30G35 Functions of hypercomplex variables and generalized variables 30G99 None of the above, but in this section |
30Gxx 普适函数论 30G06 非阿基米德函数论 [另见 12J25]；非标准函数论 [另见 03H05] 30G12 精细全纯函数与拓扑函数论 30G20 贝尔斯型与维库阿型函数的推广（伪解析、p-解析等） 30G25 离散解析函数 30G30 其他解析函数的推广（含抽象值函数） 30G35 超复变量与广义变量函数 30G99 本节不涉及上述内容 |
| 30Hxx Spaces and algebras of analytic functions of one complex variable 30H05 Spaces of bounded analytic functions of one complex variable 30H10 Hardy spaces [See also 42B30, 46E30] 30H15 Nevanlinna spaces and Smirnov spaces 30H20 Bergman spaces and Fock spaces [See also 46E30, 46E35] 30H25 Besov spaces and Qp-spaces 30H30 Bloch spaces 30H35 BMO-spaces 30H40 Zygmund spaces 30H45 de Branges-Rovnyak spaces 30H50 Algebras of analytic functions of one complex variable 30H80 Corona theorems 30H99 None of the above, but in this section |
30Hxx 复变函数解析空间与代数 30H05 复变函数有界解析空间 30H10 哈代空间 [另见 42B30,46E30] 30H15 内万林纳空间与斯米尔诺夫空间 30H20 贝格曼空间与福克空间 [另见 46E30,46E35] 30H25 贝索夫空间与Qp空间 30H30 布洛赫空间 30H35 BMO空间 30H40 西格蒙德空间 30H45 德布朗热-罗夫尼亚克空间 30H50 复变函数解析代数 30H80 冠定理 30H99 本节不涉及上述内容 |
| 30Jxx Function theory on the disc 30J05 Inner functions of one complex variable 30J10 Blaschke products 30J15 Singular inner functions of one complex variable 30J99 None of the above, but in this section |
30Jxx 离散函数论 30J05 复变函数内函数 30J10 布拉斯克积 30J15 复变函数奇异内函数 30J99 本节不涉及上述内容 |
| 30Kxx Universal holomorphic functions of one complex variable 30K05 Universal Taylor series in one complex variable 30K10 Universal Dirichlet series in one complex variable 30K15 Universal functions of one complex variable 30K20 Compositional universality 30K99 None of the above, but in this section |
30Kxx 复变函数全纯函数 30K05 复变函数泰勒级数 30K10 复变函数狄利克雷级数 30K15 复变函数泛函 30K20 复变函数复合泛函 30K99 本节不涉及上述内容 |
| 30Lxx Analysis on metric spaces 30L05 Geometric embeddings of metric spaces 30L10 Quasiconformal mappings in metric spaces 30L15 Inequalities in metric spaces 30L99 None of the above, but in this section |
30Lxx 度量空间分析 30L05 度量空间的几何嵌入 30L10 度量空间中的拟共形映射 30L15 度量空间中的不等式 30L99 本节不涉及上述内容 |
| 31-XX Potential theory {For probabilistic potential theory, see 60J45} 31-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to potential theory 31-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to potential theory 31-02 Research exposition (monographs, survey articles) pertaining to potential theory 31-03 History of potential theory [Consider also classification numbers pertaining to Section 01] 31-04 Software, source code, etc. for problems pertaining to potential theory 31-06 Proceedings, conferences, collections, etc. pertaining to potential theory 31-08 Computational methods for problems pertaining to potential theory [See also 65Exx] 31-11 Research data for problems pertaining to potential theory |
31-XX 势理论 {关于概率势理论，参见60J45} 31-00 与势理论相关的通用参考文献（手册、词典、参考书目等） 31-01 与势理论相关的入门性论述（教科书、教程论文等） 31-02 与势理论相关的研究性论述（专著、综述文章等） 31-03 势理论发展史 [另请参考第01章节的分类号] 31-04 与势理论相关问题的软件、源代码等 31-06 与势理论相关的会议论文集、学术汇编等 31-08 与势理论相关问题的计算方法 [另见65Exx] 31-11 与势理论相关问题的研究数据 |
| 31Axx Two-dimensional potential theory 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions 31A10 Integral representations, integral operators, integral equations methods in two dimensions 31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions [See also 30C85] 31A20 Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions 31A25 Boundary value and inverse problems for harmonic functions in two dimensions 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions 31A35 Connections of harmonic functions with differential equations in two dimensions 31A99 None of the above, but in this section |
31Axx 二维势理论 31A05 二维空间中的调和函数、次调和函数与超调和函数 31A10 二维空间中的积分表示、积分算子与积分方程方法 31A15 二维空间中的势函数与容量、调和测度、极值长度及相关概念[另见30C85] 31A20 二维空间中调和函数的边界行为（法图型定理等）31A25 二维空间中调和函数的边值问题与反问题 31A30 二维空间中的双调和函数、多调和函数与方程、泊松方程 31A35 二维空间中调和函数与微分方程的联系 31A99 本节不涉及上述内容 |
| 31Bxx Higher-dimensional potential theory 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 31B10 Integral representations, integral operators, integral equations methods in higher dimensions 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 31B20 Boundary value and inverse problems for harmonic functions in higher dimensions 31B25 Boundary behavior of harmonic functions in higher dimensions 31B30 Biharmonic and polyharmonic equations and functions in higher dimensions 31B35 Connections of harmonic functions with differential equations in higher dimensions 31B99 None of the above, but in this section |
31Bxx 高维势理论 31B05 高维空间中的调和函数、次调和函数与超调和函数 31B10 高维空间中的积分表示、积分算子与积分方程方法 31B15 高维空间中的势函数与容量、极值长度及相关概念 31B20 高维空间中调和函数的边值问题与反问题 31B25 高维空间中调和函数的边界行为 31B30 高维空间中的双调和方程与多调和方程及函数 31B35 高维空间中调和函数与微分方程的联系 31B99 本节不涉及上述内容 |
| 31Cxx Generalizations of potential theory 31C05 Harmonic, subharmonic, superharmonic functions on other spaces 31C10 Pluriharmonic and plurisubharmonic functions [See also 32U05] 31C12 Potential theory on Riemannian manifolds and other spaces [See also 53C20] {For Hodge theory, see 58A14} 31C15 Potentials and capacities on other spaces 31C20 Discrete potential theory 31C25 Dirichlet forms 31C35 Martin boundary theory [See also 60J50] 31C40 Fine potential theory; fine properties of sets and functions 31C45 Other generalizations (nonlinear potential theory, etc.) 31C99 None of the above, but in this section |
31Cxx 势理论的推广 31C05 其他空间上的调和函数、次调和函数与超调和函数 31C10 多调和函数与多次调和函数 [另见 32U05] 31C12 兰曼流形及其他空间上的势理论 [另见 53C20] {关于霍奇理论，参见 58A14} 31C15 其他空间上的势与容量 31C20 离散势理论 31C25 迪里克雷形式 31C35 马丁边界理论 [另见 60J50] 31C40 精细势理论；集合与函数的精细性质 31C45 其他推广（非线性势理论等） 31C99 本节不涉及上述内容 |
| 31Dxx Axiomatic potential theory 31D05 Axiomatic potential theory 31D99 None of the above, but in this section |
31Dxx 原理性潜能理论 31D05 原理性潜能理论
31D99 本节不涉及上述内容
|
| 31Exx Potential theory on fractals and metric spaces 31E05 Potential theory on fractals and metric spaces 31E99 None of the above, but in this section |
31Exx分形与度量空间的势理论 31E05 分形与度量空间的势理论
31E99 本节不涉及上述内容
|
| 32-XX Several complex variables and analytic spaces {For infinitedimensional holomorphy, see also 46G20, 58B12} 32-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to several complex variables and analytic spaces 32-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces 32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces 32-03 History of several complex variables and analytic spaces [Consider also classification numbers pertaining to Section 01] 32-04 Software, source code, etc. for problems pertaining to several complex variables and analytic spaces 32-06 Proceedings, conferences, collections, etc. pertaining to several complex variables and analytic spaces 32-08 Computational methods for problems pertaining to several complex variables and analytic spaces [See also 65Exx] 32-11 Research data for problems pertaining to several complex variables and analytic spaces |
32-XX 多个复变量与解析空间 {关于无限维全纯性，另见46G20、58B12} 32-00 关于多个复杂变量与分析空间的通用参考文献（手册、词典、参考书目等）
32-01 与复变量及解析空间相关的导论性阐述（教材、辅导论文等）
32-02 关于多个复杂变量与分析空间的研究文献（专著、综述文章）
32-03 复变数与解析空间的历史 [另参见第01节相关分类编号]
32-04 软件、源代码等，用于解决涉及多个复杂变量和解析空间的问题
32-06 与多个复变量及解析空间相关的会议记录、会议论文集等
32-08 多复变量与解析空间相关问题的计算方法 [另见 65Exx]
32-11 多个复杂变量与解析空间相关问题的研究数据
|
| 32Axx Holomorphic functions of several complex variables 32A05 Power series, series of functions of several complex variables 32A08 Polynomials and rational functions of several complex variables 32A10 Holomorphic functions of several complex variables 32A12 Multifunctions of several complex variables 32A15 Entire functions of several complex variables 32A17 Special families of functions of several complex variables 32A18 Bloch functions, normal functions of several complex variables 32A19 Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.) 32A20 Meromorphic functions of several complex variables 32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables {For geometric theory, see 32H25, 32H30} 32A25 Integral representations; canonical kernels (Szeg˝o, Bergman, etc.) 32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappi`e-type kernels) 32A27 Residues for several complex variables [See also 32C30] 32A30 Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35} 32A35 Hp -spaces, Nevanlinna spaces of functions in several complex variables [See also 32M15, 42B30, 43A85, 46J15] 32A36 Bergman spaces of functions in several complex variables 32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 32A38 Algebras of holomorphic functions of several complex variables [See also 46J10, 46J15] 32A40 Boundary behavior of holomorphic functions of several complex variables 32A45 Hyperfunctions [See also 46F15] 32A50 Harmonic analysis of several complex variables [See mainly 43-XX] 32A55 Singular integrals of functions in several complex variables 32A60 Zero sets of holomorphic functions of several complex variables 32A65 Banach algebra techniques applied to functions of several complex variables [See also 46Jxx] 32A70 Functional analysis techniques applied to functions of several complex variables [See also 46Exx] 32A99 None of the above, but in this section |
32Axx 多元全纯函数复变量 32A05 功率级数，复数级数函数可变因素 |
| 32Bxx Local analytic geometry [See also 13-XX, 14-XX] 32B05 Analytic algebras and generalizations, preparation theorems 32B10 Germs of analytic sets, local parametrization 32B15 Analytic subsets of affine space 32B20 Semi-analytic sets, subanalytic sets, and generalizations [See also 14P15] 32B25 Triangulation and topological properties of semianalytic andsubanalytic sets, and related questions 32B99 None of the above, but in this section |
32Bxx 局部解析几何 [另见13-XX, 14-XX] 32B05 分析代数与推广，预备课程定理
32B10 分析集的芽，局部参数化
32B15仿射空间的解析子集
32B20 半解析集、子解析集与推广[另见14P15]
32B25 三边测量与半解析的拓扑性质以及次解析集及相关问题
32B99 本节不涉及上述内容 |
| 32Cxx Analytic spaces 32C05 Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07] 32C07 Real-analytic sets, complex Nash functions [See also 14P15, 14P20] 32C09 Embedding of real-analytic manifolds 32C11 Complex supergeometry [See also 14A22, 14M30, 58A50] 32C15 Complex spaces 32C18 Topology of analytic spaces 32C20 Normal analytic spaces 32C22 Embedding of analytic spaces 32C25 Analytic subsets and submanifolds 32C30 Integration on analytic sets and spaces, currents [See also 32A25, 32A27] 32C35 Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30] 32C36 Local cohomology of analytic spaces 32C37 Duality theorems for analytic spaces 32C38 Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15] 32C55 The Levi problem in complex spaces; generalizations 32C81 Applications of analytic spaces to physics and other areas of science 32C99 None of the above, but in this section |
32Cxx 分析空间 32C05 实解析流形与实解析空间 [另见 14Pxx、58A07] 32C07 实解析集与复纳什函数 [另见 14P15、14P20] 32C09 实解析流形的嵌入 32C11 复超几何 [另见 14A22、14M30、58A50] 32C15 复空间 32C18 分析空间的拓扑学 32C20 正则解析空间 32C22 分析空间的嵌入 32C25 分析子集与子流形 32C30 分析集与空间上的积分、流 [另见 32A25、32A27] 32C35 分析层与上同调群 [另见 14Fxx、18F20、55N30] 32C36 分析空间的局部上同调 32C37 分析空间的对偶定理 32C38 微分算子层及其模、D-模 [另见 14F10、16S32、35A27、58J15] 32C55 复空间中的Levi问题及其推广 32C81 分析空间在物理学及其他科学领域的应用 32C99 本节不涉及上述内容 |
| 32Dxx Analytic continuation 32D05 Domains of holomorphy 32D10 Envelopes of holomorphy 32D15 Continuation of analytic objects in several complex variables 32D20 Removable singularities in several complex variables 32D26 Riemann domains 32D99 None of the above, but in this section |
32Dxx 分析延拓 32D05 全纯性域 32D10 全纯性包络 32D15 复变函数解析对象的延拓 32D20 复变函数可去奇异点 32D26 黎曼域 32D99 本节不涉及上述内容 |
| 32Exx Holomorphic convexity 32E05 Holomorphically convex complex spaces, reduction theory 32E10 Stein spaces, Stein manifolds 32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables 32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs 32E35 Global boundary behavior of holomorphic functions of several complex variables 32E40 The Levi problem 32E99 None of the above, but in this section |
32Exx 全纯凸性 32E05 全纯凸复空间的约化理论
32E10 斯坦空间，斯坦流形
32E20 多复变量中的多项式凸性、有理凸性与亚纯凸性 32E30 多复变量中的全纯函数、多项式与有理函数逼近及插值；Runge配对
32E35 多复变量全纯函数的全局边界行为 32E40 Levi问题 32E99 本节不涉及上述内容 |
| 32Fxx Geometric convexity in several complex variables 32F10 q-convexity, q-concavity 32F17 Other notions of convexity in relation to several complex variables 32F18 Finite-type conditions for the boundary of a domain 32F27 Topological consequences of geometric convexity 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.) 32F45 Invariant metrics and pseudodistances in several complex variables 32F99 None of the above, but in this section |
32Fxx 复变函数中的几何凸性 32F10 q-凸性与q-凹性 32F17 复变函数中其他凸性概念 32F18 域边界的有限型条件 32F27 几何凸性的拓扑性质 32F32 几何凸性的解析性质（消失定理等） 32F45 复变函数中的不变度量与伪距离 32F99 本节不涉及上述内容 |
| 32Gxx Deformations of analytic structures 32G05 Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15] 32G07 Deformations of special (e.g., CR) structures 32G08 Deformations of fiber bundles 32G10 Deformations of submanifolds and subspaces 32G13 Complex-analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 32G15 Moduli of Riemann surfaces, Teichmu¨ller theory (complex-analytic aspects in several variables) [See also 14H15, 30Fxx] 32G20 Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30] 32G34 Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) [See also 34Mxx] 32G81 Applications of deformations of analytic structures to the sciences 32G99 None of the above, but in this section |
32Gxx 分析结构的形变
32G05 复结构的形变 [另见 13D10、16S80、58H10、58H15] |
| 32Hxx Holomorphic mappings and correspondences 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 32H04 Meromorphic mappings in several complex variables 32H12 Boundary uniqueness of mappings in several complex variables 32H25 Picard-type theorems and generalizations for several complex variables {For function-theoretic properties, see 32A22} 32H30 Value distribution theory in higher dimensions {For function-theoretic properties, see 32A22} 32H35 Proper holomorphic mappings, finiteness theorems 32H40 Boundary regularity of mappings in several complex variables 32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables 32H99 None of the above, but in this section |
32Hxx 全纯映射与对应关系 32H02 复变函数中的全纯映射、（全纯）嵌入及相关问题 32H04 复变函数中的亚全纯映射 32H12 复变函数映射的边界唯一性 32H25 复变函数的皮卡型定理及其推广（函数论性质参见32A22） 32H30 高维值分布理论（函数论性质参见32A22） 32H35 真全纯映射与有限性定理 32H40 复变函数映射的边界正则性 32H50 复变函数全纯映射的迭代、不动点及相关问题 32H99 本节不涉及上述内容 |
| 32Jxx Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx} 32J05 Compactification of analytic spaces 32J10 Algebraic dependence theorems 32J15 Compact complex surfaces 32J17 Compact complex 3-folds 32J18 Compact complex n-folds 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects) [See also 14C30] 32J27 Compact K¨ahler manifolds: generalizations, classification 32J81 Applications of compact analytic spaces to the sciences 32J99 None of the above, but in this section |
32Jxx 紧致解析空间 {关于黎曼曲面的理论，参见14Hxx、30Fxx；代数理论相关内容，参见14Jxx} |
| 32Kxx Generalizations of analytic spaces 32K05 Banach analytic manifolds and spaces [See also 46G20, 58Bxx] 32K07 Formal and graded complex spaces [See also 58C50] 32K12 Holomorphic maps with infinite-dimensional arguments or values [See also 46G20] 32K15 Differentiable functions on analytic spaces, differentiable spaces [See also 58C25] 32K99 None of the above, but in this section 32Lxx Holomorphic fiber spaces [See also 55Rxx] 32L05 Holomorphic bundles and generalizations 32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F06, 14H60, 14J60, 18F20, 55N30] 32L15 Bundle convexity [See also 32F10] 32L20 Vanishing theorems 32L25 Twistor theory, double fibrations (complexanalytic aspects) [See also 53C28] 32L81 Applications of holomorphic fiber spaces to the sciences 32L99 None of the above, but in this section |
32Kxx解析空间的推广 32K05 Banach解析流形与空间 [另见46G20、58Bxx]
32K07 形式化与分级复空间 [另见58C50] 32K12 无限维参数或值的全纯映射 [另见46G20] 32K15 分析空间与可微空间上的可微函数 [另见58C25] 32K99 上述均非，但本节32Lxx 全纯纤维空间 [另见55Rxx] 32L05 全纯丛及其推广 32L10 全纯向量丛层与截面上同调的普遍结果 [另见14F06、14H60、14J60、18F20、55N30] 32L15 丛凸性 [另见32F10] 32L20 消失定理 32L25 扭量理论与双纤维化（复解析方面）[另见53C28] 32L81 全纯纤维空间在科学中的应用 32L99 本节不涉及上述内容 |
| 32Mxx Complex spaces with a group of automorphisms 32M05 Complex Lie groups, group actions on complex spaces [See also 22E10] 32M10 Homogeneous complex manifolds [See also 14M17, 57T15] 32M12 Almost homogeneous manifolds and spaces [See also 14M17] 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) [See also 22E10, 22E40, 53C35, 57T15] 32M17 Automorphism groups of C n and affine manifolds 32M18 Automorphism groups of other complex spaces 32M25 Complex vector fields, holomorphic foliations, Cactions 32M99 None of the above, but in this section |
32Mxx具有自同构群的复空间 32M05 复Lie群，群在复空间上的作用 [另见22E10]
32M10 同质复流形 [另见 14M17,57T15]
32M12 几乎齐性流形与空间 [另见 14M17]
32M15 赫米特对称空间、有界对称域、若尔当代数（复解析特性）[另见 22E10、22E40、53C35、57T15]
32M17 C n的自同构群与仿射流形
32M18 其他复空间的自同构群
32M25 复向量场、全纯叶状结构、C作用
32M99 本节不涉及上述内容
|
| 32Nxx Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35] 32N05 General theory of automorphic functions of several complex variables 32N10 Automorphic forms in several complex variables 32N15 Automorphic functions in symmetric domains 32N99 None of the above, but in this section |
32Nxx 自守函数 [另见 11Fxx、20H10、22E40、30F35] 32N05 多复变量自守函数通论 32N10 多复变量自守形式 32N15 对称域中的自守函数 32N99 本节不涉及上述内容 |
| 32Pxx Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32P05 Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32P99 None of the above, but in this section |
32Pxx 非阿基米德分析（还应分配至少一个来自第32节的其他分类编号，该章节描述了问题类型） 32P05 非阿基米德分析（还应分配至少一个来自第32节的其他分类编号，该章节描述了问题类型） 32P99 本节不涉及上述内容 |
| 32Qxx Complex manifolds 32Q02 Special domains (Reinhardt, Hartogs, circular, tube, etc.) in C n and complex manifolds 32Q05 Negative curvature complex manifolds 32Q10 Positive curvature complex manifolds 32Q15 K¨ahler manifolds 32Q20 K¨ahler-Einstein manifolds [See also 53Cxx] 32Q25 Calabi-Yau theory (complex-analytic aspects) [See also 14J32] 32Q26 Notions of stability for complex manifolds 32Q28 Stein manifolds 32Q30 Uniformization of complex manifolds 32Q35 Complex manifolds as subdomains of Euclidean space 32Q40 Embedding theorems for complex manifolds 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 32Q55 Topological aspects of complex manifolds 32Q56 Oka principle and Oka manifolds 32Q57 Classification theorems for complex manifolds 32Q60 Almost complex manifolds 32Q65 Pseudoholomorphic curves 32Q99 None of the above, but in this section |
32Qxx 复流形 32Q02 特殊结构域（Reinhardt、Hartogs、环状结构）导管等)在C中n维复流形
32Q05 负曲率复流形
32Q10 正曲率复流形
32Q15凯勒流形
32Q20 卡勒-爱因斯坦流形 [另见 53Cxx]
32Q25 Calabi-Yau理论（复分析方面）[另见14J32]
32Q26 复流形的稳定性概念
32Q28 斯坦流形
32Q30 复流形的统一化
32Q35 复流形作为欧氏空间的子域空间复流形的32Q40嵌入定理
32Q45双曲流形和小林双曲流形
32Q55 复流形的拓扑性质 32Q56 Oka原理与Oka流形复流形的
32Q57分类定理 32Q60 几乎复流形
32Q65 假全纯曲线
32Q99 本节不涉及上述内容
|
| 32Sxx Complex singularities [See also 58Kxx] 32S05 Local complex singularities [See also 14J17] 32S10 Invariants of analytic local rings 32S15 Equisingularity (topological and analytic) [See also 14E15] 32S20 Global theory of complex singularities; cohomological properties [See also 14E15] 32S22 Relations with arrangements of hyperplanes [See also 52C35] 32S25 Complex surface and hypersurface singularities [See also 14J17] 32S30 Deformations of complex singularities; vanishing cycles [See also 14B07] 32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects) [See also 14C30, 14D07] 32S40 Monodromy; relations with differential equations and D-modules (complex-analytic aspects) 32S45 Modifications; resolution of singularities (complex-analytic aspects) [See also 14E15] 32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants 32S55 Milnor fibration; relations with knot theory [See also 57K10, 57K45] 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) [See also 58Kxx] 32S65 Singularities of holomorphic vector fields and foliations 32S70 Other operations on complex singularities 32S99 None of the above, but in this section |
32Sxx 复变奇点 [另见58Kxx] 32S05 局部复数奇点 [另见 14J17]
32S10解析局部环的不变量 32S15 等奇异（拓扑与解析）[另见 14E15]
32S20 复变奇点的全局理论；上同调特性 [另见14E15]
32S22 与超平面排列的关系[另见52C35]
32S25 复面与超曲面奇点[另见14J17]
32S30 复变奇点的形变；消失周期 [另见 14B07]
32S35奇异簇的混合Hodge理论（复解析方面）[另见14C30、14D07]
32S40单值性；与微分方程及D-模的关系（复解析方面） 32S45 修正；奇点解析（复分析方面）[另见14E15]
32S50 复变奇点的拓扑学特性：Lef-schetz定理，拓扑分类，不变量
32S55 米尔诺纤维化；与纽结理论的关系[另见57K10,57K45]
32S60 分层；可构造层；交上同调（复分析方面）[另见58Kxx]
32S65全纯向量场与叶状结构的奇点
32S70 复奇点的其他运算
32S99 本节不涉及上述内容
|
| 32Txx Pseudoconvex domains 32T05 Domains of holomorphy 32T15 Strongly pseudoconvex domains 32T20 Worm domains 32T25 Finite-type domains 32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries 32T35 Exhaustion functions 32T40 Peak functions 32T99 None of the above, but in this section |
32Txx 伪凸域 32T05 全纯域 32T15 强伪凸域 32T20 蠕虫域 32T25 有限型域 32T27 弱伪凸边界上的几何与解析不变量 32T35 消耗函数 32T40 峰函数 32T99 本节不涉及上述内容 |
| 32Uxx Pluripotential theory 32U05 Plurisubharmonic functions and generalizations [See also 31C10] 32U10 Plurisubharmonic exhaustion functions 32U15 General pluripotential theory 32U20 Capacity theory and generalizations 32U25 Lelong numbers 32U30 Removable sets in pluripotential theory 32U35 Plurisubharmonic extremal functions, pluricomplex Green functions 32U40 Currents 32U99 None of the above, but in this section |
32Uxx 多潜能理论 32U05 多次调和函数及其推广[另见31C10] 32U10 多次调和耗竭函数 32U15 一般多潜能理论 32U20 容量理论及其推广 32U25 莱隆数 32U30 多潜能理论中的可去集 32U35 多次调和极值函数与复格林函数 32U40 电流 32U99 本节不涉及上述内容 |
| 32Vxx CR manifolds 32V05 CR structures, CR operators, and generalizations 32V10 CR functions 32V15 CR manifolds as boundaries of domains 32V20 Analysis on CR manifolds 32V25 Extension of functions and other analytic objects from CR manifolds 32V30 Embeddings of CR manifolds 32V35 Finite-type conditions on CR manifolds 32V40 Real submanifolds in complex manifolds 32V99 None of the above, but in this section |
32Vxx CR流形 32V05 CR结构、CR算子及其推广 32V10 CR函数 32V15 作为域边界的CR流形 32V20 CR流形分析 32V25 函数及其他解析对象在CR流形上的延拓 32V30 CR流形的嵌入 32V35 CR流形的有限型条件 32V40 复流形中的实子流形 32V99 本节不涉及上述内容 |
| 32Wxx Differential operators in several variables 32W05 ∂ and ∂-Neumann operators 32W10 ∂b and ∂b-Neumann operators 32W20 Complex Monge-Amp`ere operators 32W25 Pseudodifferential operators in several complex variables 32W30 Heat kernels in several complex variables 32W50 Other partial differential equations of complex analysis in several variables 32W99 None of the above, but in this section |
32Wxx 多变量微分算子 32W05 ∂和∂-诺伊曼算子 32W10 ∂b和∂b-诺伊曼算子 32W20 复变蒙日-安培算子 32W25 多复变量伪微分算子 32W30 多复变量热核 32W50 其他多变量复变分析偏微分方程 32W99 本节不涉及上述内容 |
| 33-XX Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11- XX; for representation theory, see 22Exx} 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions 33-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions 33-02 Research exposition (monographs, survey articles) pertaining to special functions 33-03 History of special functions [Consider also classification numbers pertaining to Section 01] 33-04 Software, source code, etc. for problems pertaining to special functions 33-06 Proceedings, conferences, collections, etc. pertaining to special functions 33-11 Research data for problems pertaining to special functions |
33-XX 特殊函数（33-XX研究函数作为函数的性质）{正交函数参见42Cxx；组合学相关参见05Axx；数论相关参见11-XX；表示论相关参见22Exx} 33-00 与特殊函数相关的通用参考文献（手册、词典、参考书目等） 33-01 与特殊函数相关的入门性论述（教科书、教程论文等） 33-02 与特殊函数相关的研究性论述（专著、综述文章等） 33-03 特殊函数的历史沿革[另请参考第01节的分类编号] 33-04 与特殊函数相关问题的软件、源代码等资源 33-06 与特殊函数相关的会议论文集、学术汇编等 33-11 与特殊函数相关问题的研究数据 |
| 33Bxx Elementary classical functions 33B10 Exponential and trigonometric functions 33B15 Gamma, beta and polygamma functions 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) 33B30 Higher logarithm functions 33B99 None of the above, but in this section |
33Bxx 基础经典函数 33B10 指数与三角函数 33B15 γ、β及多γ函数 33B20 不完全β与γ函数（误差函数、概率积分、菲涅尔积分） 33B30 高阶对数函数 33B99 本节不涉及上述内容 |
| 33Cxx Hypergeometric functions 33C05 Classical hypergeometric functions, 2F1 33C10 Bessel and Airy functions, cylinder functions, 0F1 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1 33C20 Generalized hypergeometric series, pFq 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) {For general orthogonal polynomials and functions, see also 42C05} 33C47 Other special orthogonal polynomials and functions 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable 33C52 Orthogonal polynomials and functions associated with root systems 33C55 Spherical harmonics 33C60 Hypergeometric integrals and functions defined by them (E, G, H and I functions) 33C65 Appell, Horn and Lauricella functions 33C67 Hypergeometric functions associated with root systems 33C70 Other hypergeometric functions and integrals in several variables 33C75 Elliptic integrals as hypergeometric functions 33C80 Connections of hypergeometric functions with groups and algebras, and related topics 33C90 Applications of hypergeometric functions 33C99 None of the above, but in this section |
33Cxx 超几何函数 33C05 经典超几何函数，2F1 33C10 贝塞尔函数与艾里函数、柱面函数，0F1 33C15 融合超几何函数、惠特克函数，1F1 33C20 广义超几何级数，pFq 33C45 正交多项式与超几何型函数（雅可比、拉盖尔、埃尔米特、阿斯基方案等）{关于一般正交多项式与函数，另见42C05} 33C47 其他特殊正交多项式与函数 33C50 可用单变量特殊函数表示的多变量正交多项式与函数 33C52 与根系相关的正交多项式与函数 33C55 球面调和函数 33C60 超几何积分及其定义的函数（E、G、H和I函数） 33C65 阿佩尔函数、霍恩函数与劳里切拉函数 33C67 与根系相关的超几何函数 33C70 多变量其他超几何函数与积分 33C75 椭圆积分作为超几何函数 33C80 超几何函数与群代数的联系及相关课题 33C90 超几何函数的应用 33C99 本节不涉及上述内容 |
| 33Dxx Basic hypergeometric functions 33D05 q-gamma functions, q-beta functions and integrals 33D15 Basic hypergeometric functions in one variable, rφs 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) 33D60 Basic hypergeometric integrals and functions defined by them 33D65 Bibasic functions and multiple bases 33D67 Basic hypergeometric functions associated with root systems 33D70 Other basic hypergeometric functions and integrals in several variables 33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics 33D90 Applications of basic hypergeometric functions 33D99 None of the above, but in this section |
33Dxx 基本超几何函数 33D05 q-伽马函数、q-贝塔函数及积分 33D15 一元基本超几何函数与 rφs 33D45 基本正交多项式与函数（如Askey-Wilson多项式等） 33D50 可用一元基本超几何函数表示的多变量正交多项式与函数 33D52 与根系相关的基正交多项式及函数（如Macdonald多项式等） 33D60 基本超几何积分及其定义的函数 33D65 双基函数与多重基 33D67 与根系相关的基本超几何函数 33D70 多变量其他基本超几何函数与积分 33D80 基本超几何函数与量子群、Chevalley群、p进群、Hecke代数及相关主题的联系 33D90 基本超几何函数的应用 33D99 本节不涉及上述内容 |
| 33Exx Other special functions 33E05 Elliptic functions and integrals 33E10 Lam´e, Mathieu, and spheroidal wave functions 33E12 Mittag-Leffler functions and generalizations 33E15 Other wave functions 33E17 Painlev´e-type functions 33E20 Other functions defined by series and integrals 33E30 Other functions coming from differential, difference and integral equations 33E50 Special functions in characteristic p (gamma functions, etc.) 33E99 None of the above, but in this section |
33Exx 其他特殊函数 33E05 椭圆函数与积分 33E10 拉梅函数、马蒂厄函数及球面波函数 33E12 米塔格-莱夫勒函数及其推广形式 33E15 其他波函数 33E17 帕涅列夫型函数 33E20 由级数与积分定义的其他函数 33E30 源自微分方程、差分方程及积分方程的其他函数 33E50 特征参数p的特殊函数（如伽马函数等） 33E99 本节不涉及上述内容 |
| 33Fxx Computational aspects of special functions {For software etc., see 33-04} 33F05 Numerical approximation and evaluation of special functions [See also 65D20] 33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) [See also 68W30] 33F99 None of the above, but in this section |
33Fxx 特殊函数的计算方法（软件相关请参见33-04） 33F05 特殊函数的数值逼近与计算[另见65D20] 33F10 特殊函数的符号计算（戈斯珀算法、蔡尔伯格算法等）[另见68W30] 33F99 本节不涉及上述内容 |
| 34-XX Ordinary differential equations 34-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordinary differential equations 34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34-03 History of ordinary differential equations [Consider also classification numbers pertaining to Section 01] 34-04 Software, source code, etc. for problems pertaining to ordinary differential equations 34-06 Proceedings, conferences, collections, etc. pertaining to ordinary differential equations 34-11 Research data for problems pertaining to ordinary differential equations |
34-XX 常微分方程 34-00 常微分方程相关通用参考文献（手册、词典、书目等） 34-01 常微分方程入门教材（教科书、教程论文等） 34-02 常微分方程研究专著（专著、综述文章等） 34-03 常微分方程发展史[另见01章节分类号] 34-04 常微分方程相关问题的软件、源代码等 34-06 常微分方程相关会议论文集、学术汇编等 34-11 常微分方程相关问题的研究数据 |
| 34Axx General theory for ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations 34A06 Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) 34A07 Fuzzy ordinary differential equations 34A08 Fractional ordinary differential equations and fractional differential inclusions 34A09 Implicit ordinary differential equations, differential-algebraic equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. [See also 44-XX] 34A26 Geometric methods in ordinary differential equations 34A30 Linear ordinary differential equations and systems, general 34A33 Ordinary lattice differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory 34A35 Ordinary differential equations of infinite order 34A36 Discontinuous ordinary differential equations 34A37 Ordinary differential equations with impulses 34A38 Hybrid systems of ordinary differential equations 34A40 Differential inequalities involving functions of a single real variable [See also 26D20] 34A45 Theoretical approximation of solutions to ordinary differential equations {For numerical analysis, see 65Lxx} 34A55 Inverse problems involving ordinary differential equations 34A60 Ordinary differential inclusions [See also 49J21, 49K21] 34A99 None of the above, but in this section |
34Axx 常微分方程通论 34A05 常微分方程显式解与初等积分 34A06 广义常微分方程（测度微分方程、集合值微分方程等） 34A07 模糊微分方程 34A08 分式微分方程与分式微分包含关系 34A09 隐微分方程与微分代数方程 34A12 常微分方程初值问题：解的存在性、唯一性、连续依赖性与延拓性 34A25 常微分方程解析理论：级数、变换、运算、算子等[另见44-XX] 34A26 常微分方程几何方法 34A30 线性常微分方程与系统（通论） 34A33 常格微分方程 34A34 非线性常微分方程与系统（通论） 34A35 无限阶常微分方程 34A36 不连续常微分方程 34A37 带冲量的常微分方程 34A38 常微分方程混合系统 34A40 单变量函数微分不等式[另见26D20] 34A45 常微分方程解的理论逼近{数值分析参见65Lxx} 34A55 常微分方程逆问题 34A60 常微分包含关系[另见49J21]49K21] 34A99 本节不涉及上述内容 |
| 34Bxx Boundary value problems for ordinary differential equations {For ordinary differential operators, see 34Lxx} 34B05 Linear boundary value problems for ordinary differential equations 34B07 Linear boundary value problems for ordinary differential equations with nonlinear dependence on the spectral parameter 34B08 Parameter dependent boundary value problems for ordinary differential equations 34B09 Boundary eigenvalue problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B20 Weyl theory and its generalizations for ordinary differential equations 34B24 Sturm-Liouville theory [See also 34Lxx] 34B27 Green’s functions for ordinary differential equations 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34B37 Boundary value problems with impulses for ordinary differential equations 34B40 Boundary value problems on infinite intervals for ordinary differential equations 34B45 Boundary value problems on graphs and networks for ordinary differential equations 34B60 Applications of boundary value problems involving ordinary differential equations 34B99 None of the above, but in this section |
34Bxx 常微分方程的边界值问题 {关于常微分算子的讨论，请参见34Lxx} 34B05 常微分方程的线性边界值问题 34B07 光谱参数非线性依赖的常微分方程线性边界值问题 34B08 常微分方程的参数依赖边界值问题 34B09 常微分方程的边界特征值问题 34B10 常微分方程的非局部与多点边界值问题 34B15 常微分方程的非线性边界值问题 34B16 常微分方程的奇异非线性边界值问题 34B18 常微分方程非线性边界值问题的正解 34B20 常微分方程的Weyl理论及其推广 34B24 Sturm-Liouville理论 [另见34Lxx] 34B27 常微分方程的格林函数 34B30 特殊常微分方程（马蒂厄、希尔、贝塞尔等） 34B37 常微分方程的脉冲边界值问题 34B40 常微分方程的无限区间边界值问题 34B45 常微分方程的图与网络边界值问题 34B60 常微分方程边界值问题的应用 34B99 本节不涉及上述内容 |
| 34Cxx Qualitative theory for ordinary differential equations [See also 37-XX] 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations 34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34C12 Monotone systems involving ordinary differential equations 34C14 Symmetries, invariants of ordinary differential equations [See also 37C79] 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms 34C23 Bifurcation theory for ordinary differential equations [See also 37Gxx] 34C25 Periodic solutions to ordinary differential equations 34C26 Relaxation oscillations for ordinary differential equations 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations [See also 37Dxx] 34C29 Averaging method for ordinary differential equations 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 34C40 Ordinary differential equations and systems on manifolds 34C41 Equivalence and asymptotic equivalence of ordinary differential equations 34C45 Invariant manifolds for ordinary differential equations 34C46 Multifrequency systems of ordinary differential equations 34C55 Hysteresis for ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 34C99 None of the above, but in this section |
34Cxx 常微分方程定性理论 [另见37-XX] 34C05 积分曲线拓扑结构、奇点与常微分方程极限环 34C07 多项式及解析向量场极限环理论（存在性、唯一性、界值、希尔伯特第16问题及其分支）在常微分方程中的应用 34C08 常微分方程与实代数几何的联系（多项式、去奇异化、阿贝尔积分零点等） 34C10 常微分方程振荡理论、零点、解的非共轭性及比较理论 34C11 常微分方程解的增长与有界性 34C12 涉及常微分方程的单调系统 34C14 常微分方程的对称性与不变量 [另见37C79] 34C15 常微分方程的非线性振荡与耦合振子 34C20 常微分方程与系统的变换与约化 34C23 常微分方程的分岔理论[另见37Gxx] 34C25 常微分方程的周期解 34C26 常微分方程的弛豫振荡 34C27 常微分方程的近似周期与伪近似周期解 34C28 常微分方程的复杂行为与混沌系统[另见37Dxx] 34C29 常微分方程的平均化方法 34C37 常微分方程的同宿与异宿解 34C40 流形上的常微分方程与系统 34C41 常微分方程的等价性与渐近等价性 34C45 常微分方程的不变流形 34C46 常微分方程的多频系统 34C55 常微分方程的迟滞现象 34C60 常微分方程模型的定性研究与仿真 34C99 本节不涉及上述内容 |
| 34Dxx Stability theory for ordinary differential equations [See also 37C75, 93Dxx] 34D05 Asymptotic properties of solutions to ordinary differential equations 34D06 Synchronization of solutions to ordinary differential equations 34D08 Characteristic and Lyapunov exponents of ordinary differential equations 34D09 Dichotomy, trichotomy of solutions to ordinary differential equations 34D10 Perturbations of ordinary differential equations 34D15 Singular perturbations of ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations [See also 37C20] 34D35 Stability of manifolds of solutions to ordinary differential equations 34D45 Attractors of solutions to ordinary differential equations [See also 37C70, 37D45] 34D99 None of the above, but in this section |
34Dxx 常微分方程稳定性理论 [另见 37C75,93Dxx] 34D05 常微分方程解的渐近性质 34D06 常微分方程解的同步性 34D08 常微分方程特征值与李雅普诺夫指数 34D09 常微分方程解的二分法与三分法 34D10 常微分方程的摄动 34D15 常微分方程的奇异摄动 34D20 常微分方程解的稳定性 34D23 常微分方程解的全局稳定性 34D30 常微分方程解的结构稳定性与类似概念 [另见 37C20] 34D35 常微分方程解流形的稳定性 34D45 常微分方程解的吸引子 [另见 37C70,37D45] 34D99 本节不涉及上述内容 |
| 34Exx Asymptotic theory for ordinary differential equations 34E05 Asymptotic expansions of solutions to ordinary differential equations 34E10 Perturbations, asymptotics of solutions to ordinary differential equations 34E13 Multiple scale methods for ordinary differential equations 34E15 Singular perturbations, general theory for ordinary differential equations 34E17 Canard solutions to ordinary differential equations 34E18 Methods of nonstandard analysis for ordinary differential equations 34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations 34E99 None of the above, but in this section |
34Exx 常微分方程渐近理论 34E05 常微分方程解的渐近展开 34E10 常微分方程解的摄动与渐近性 34E13 常微分方程多尺度方法 34E15 奇异性摄动与常微分方程一般理论 34E17 常微分方程的卡纳德解 34E18 常微分方程非标准分析方法 34E20 奇异性摄动、拐点理论与常微分方程 WKB 方法 34E99 本节不涉及上述内容 |
| 34Fxx Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03] 34F05 Ordinary differential equations and systems with randomness [See also 34K50, 60H10, 93E03] 34F10 Bifurcation of solutions to ordinary differential equations involving randomness 34F15 Resonance phenomena for ordinary differential equations involving randomness 34F99 None of the above, but in this section |
34Fxx 常微分方程与随机系统 [另见 34K50、60H10、93E03] 34F05 常微分方程与随机系统 [另见 34K50、60H10、93E03] 34F10 随机常微分方程解的分岔现象 34F15 随机常微分方程的共振现象 34F99 本节不涉及上述内容 |
| 34Gxx Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] 34G10 Linear differential equations in abstract spaces [See also 47D06, 47D09] 34G20 Nonlinear differential equations in abstract spaces [See also 47Hxx, 47Jxx] 34G25 Evolution inclusions 34G99 None of the above, but in this section |
34Gxx 抽象空间中的微分方程 [另见 34Lxx、37Kxx、47Dxx、47Hxx、47Jxx、58D25] 34G10 抽象空间中的线性微分方程 [另见 47D06、47D09] 34G20 抽象空间中的非线性微分方程 [另见 47Hxx、47Jxx] 34G25 演化包含 34G99 本节不涉及上述内容 |
| 34Hxx Control problems including ordinary differential equations [See also 49J15, 49K15, 93C15] 34H05 Control problems involving ordinary differential equations [See also 49J15, 49K15, 93C15] 34H10 Chaos control for problems involving ordinary differential equations 34H15 Stabilization of solutions to ordinary differential equations 34H20 Bifurcation control of ordinary differential equations 34H99 None of the above, but in this section |
34Hxx 包含常微分方程的控制问题 [另见 49J15、49K15、93C15] 34H05 涉及常微分方程的控制问题 [另见 49J15、49K15、93C15] 34H10 涉及常微分方程的混沌控制 34H15 常微分方程解的稳定化 34H20 常微分方程的分岔控制 34H99 本节不涉及上述内容 |
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